Using methods previously applied to product life cycles, this paper models developer engagement through the project life cycle for open-source projects, and detects similar dynamics in a cross section of projects. Endogenous growth theory is used to model growth dynamics in open-source software engineering, while incorporating the interactions between growth levels and developer activity over time using systems of differential equations. The solution to this model calibrates well to many open-source projects. The model generates an estimate of the lifetime developer engagement and growth, which supports estimating a lifetime production value of open-source projects.
@article{arxiv.2605.12738,
title = {Project Life Cycles in Open-Source Software},
author = {Sanjiv Das and Andrii Ieroshenko and Piyush Jain and David Qiu and Michael Chin and Brian Granger},
journal= {arXiv preprint arXiv:2605.12738},
year = {2026}
}